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Electrical conductivity in granular media and Branly’s coherer: A simple experiment Eric Falcon∗ and Bernard Castaing Laboratoire de Physique, Ecole´ Normale Sup´erieure de Lyon, UMR 5672, 46, all´ee d’Italie, 69 007 Lyon, France (Dated: October 25, 2018) We show how a simple laboratory experiment can illustrate certain electrical transport properties of metallic granular media. At a low critical external voltage, a transition from an insulating to a conductive state is observed. This transition comes from an electro-thermal coupling in the vicinity of the microcontacts between grains where microwelding occurs. Our apparatus allows us to obtain an implicit determination of the microcontact temperature, which is analogous to the use of a resistive thermometer. The experiment also illustrates an old problem, the explanation of Branly’s coherer effect – a radio wave detector used for the first wireless radio transmission, and based on the sensitivity of the metal fillings conductivity to an electromagnetic wave. I. INTRODUCTION II. A BRIEF HISTORICAL REVIEW In 1887, shortly after the publication of Maxwell’s the- The coherer or Branly effect is an electrical conduction ory of electromagnetism, experiments performed by H. instability that appears in a slightly oxidized metallic Hertz clearly demonstrated the free space generation and powder under a constraint.1 The initial high powder re- propagation of electromagnetic waves. He noticed that sistance falls irreversibly by several orders of magnitude sparks (high frequency electromagnetic waves of the or- der of 100 MHz) could induce arcing across a wire loop as soon as an electromagnetic wave is produced in its 10,11 vicinity. The effect was discovered in 1890 by E. Branly1 containing a small gap, a few meters away. and is related to other phenomena. For instance, a tran- This discovery was anticipated by many people; P. S. sition from an insulating state to a conducting state is Munk observed in 1835 the permanent increase of the observed as the external source exceeds a threshold volt- electrical conductivity of a mixture of metal filings re- sulting from the passage of a discharge current of a Ley- age (the DC Branly effect); temporal fluctuations and 12 slow relaxations of resistance also occur under certain den jar. In 1879 D. E. Hughes observed a similar phe- conditions.2 nomenon for a loose contact formed of a carbon rod rest- ing in the grooves in two carbon blocks, and with a tube filled with metallic granules (a microphone because it was Although these electrical transport phenomena in first designed to detect acoustic waves). Hughes appears metallic granular media were involved in the first wireless to have discovered the important fact that such a tube radio transmission near 1900, they still are not well un- was sensitive to electric sparks at a distance as indicated derstood. Several possible processes at the contact scale by its sudden change in conductivity. At the time, the have been invoked without a clear verification: electrical 3 Royal Society of London was not convinced, and his re- breakdown of the oxide layers on grains, the modified sults were published some 20 years later,13 a long time af- tunnel effect through the metal-oxide/semiconductor- ter the discovery of hertzian waves. In 1884 T. Calzecchi- metal junction,4 the attraction of grains by molecular or 5 Onesti performed experiments on the behavior of metallic electrostatic forces, and local welding of microcontacts powders under the action of various electromotive forces, by a Joule heating effect.4,6,7 A global process of percola- 3,5,6 and observed a considerable increase of the powder con- tion within the grain assembly also has been invoked. ductivity by successively opening and closing a circuit containing an induction coil and a tube with fillings.14 Our goal in this paper is to understand the DC Branly The action of nearby electromagnetic waves on metallic effect by means of an experiment with a chain of metallic powders was observed and extensively studied by Branly beads.8 Our focus is on the local properties (the contacts in 1890.1 When metallic filings are loosely arranged be- arXiv:cond-mat/0407773v2 [cond-mat.other] 16 Nov 2004 between grains) instead of the collective properties. We tween two electrodes in a glass or ebonite tube, it has a also discuss the history of the electrical and thermal prop- very high initial resistance of many megohms due to an erties of non-homogeneous media such as granular media, oxide layer likely present on the particle surfaces. When as well as the influence of electromagnetic waves on their an electric spark was generated at a distance away, the re- conductance.9 After a brief review of the history of the sistance was suddenly reduced to several ohms. This con- coherer effect in Sec. II, we introduce in Sec. IIIA an ex- ductive state remained until the tube was tapped restor- periment that can be easily done in a standard physics ing the resistance to its earlier high value. Because the laboratory. We present our results in Sec. III B, followed electron was not known at this time (it was discovered in by a qualitative and quantitative interpretation of the 1897),15 Branly called his device a “radio conductor” to conduction transition mechanism in Secs. III C and III D. recall that “the powder conductivity increased under the Our conclusions are given in Sec. IV. influence of the electric radiations from the spark;” the 2 meaning of the prefix “radio” at this time was “radiant” sualization (with an infrared camera) of the conduction or “radiation.” He performed other experiments with paths when a very high voltage (> 500 V) was applied various powders, lightly or tightly compressed, and found to a monolayer of aluminium beads.6 More recently, the that the same effect occurred for two metallic beads in action at a distance of sparks was investigated.7 For ad- contact, and for two slightly oxidized steel or copper wires ditional information about the history of the coherer, see lying across each other with light pressure.16 This loose Refs. 21 and 22. or imperfect contact was found to be extremely sensitive to a distant electric spark. This discovery caused a considerable stir when O. III. ELECTRICAL CONDUCTIVITY OF A CHAIN OF METALLIC BEADS Lodge in 1894 repeated and extended Hertz’s experi- ments by using a Branly tube, a much more sensitive detector than the wire loop used by Hertz.11,14 Lodge Understanding the electrical conduction transition in improved the Branly tube so that it was a reliable, re- granular materials is a complicated problem that depends producible detector, and automated it by tapping on on many parameters: the statistical distribution of the the tube with a slight mechanical shock. Lodge called shape and size of the grains, the applied force, and the this electromagnetic wave detector a “coherer” from the local properties at the contact scale of two grains, that Latin cohaerere, which means “stick together.” He said is, the degree of oxidization, surface state, and rough- that the fillings “coherered” under the action of the elec- ness. Among the phenomena proposed to explain the tromagnetic wave and needed to be “decoherered” by a coherer effect, it is easy to show that some have only shock. Later, Branly and Lodge focused their fundamen- a secondary contribution. For instance, because the co- tal research on mechanisms of powder conductivity, and herer effect was observed by Branly with a single contact 16 not on practical applications such as wireless communica- between two grains, percolation cannot be the domi- tions. However, based on using the coherer as a wave de- nant mechanism. Moreover, when two beads in contact tector, the first wireless telegraphy communications were are connected in series with a battery, a coherer effect 19 transmitted in 1895 by G. Marconi, and independently is observed at a sufficiently high imposed voltage, in a by A. S. Popov.12,14,17 Popov also used the coherer to way similar to the action at a distance of a spark or an detect atmospheric electrical discharges at a distance. electromagnetic wave. We will reduce the number of pa- Lodge first hypothesized that the metallic grains were rameters, without loss of generality, by focusing on elec- welded together by the action of the voltages that are trical transport within a chain of metallic beads directly induced by electromagnetic waves.14 According to some connected to a DC electrical source. including Lodge,14,18 the grains became dipoles and at- Computer U, I, R tracted each other by electrostatic forces, inducing grains + I to stick together, thus forming conductive chains. A - Force F shock should be enough to break these fragile chains and Displacement x to restore the resistance to its original value. Branly did Stepper motor 1 N Force Force not believe this hypothesis, and to demonstrate that mo- sensor 0 x tion of the grains was not necessary, he immersed the par- F < 500 N PVC ticles in wax or resin. He also used a column of six steel balls or disks, which were a few centimeters in diameter. FIG. 1: Schematics of experimental setup. Because the coherer effect persisted, he thought that the properties of the dielectric between the grains played an important role. In 1900, Guthe et al. performed sim- ilar experiments with two balls in contact.19 However, A. Experimental setup the invention by de Forest of the triode in 1906, the first vacuum tube (an audion), supplanted the coherer as a The experimental setup is sketched in Fig. 1. It con- receiver, and Branly’s effect sank into oblivion without sists of a chain of 50 identical stainless steel beads,23 being fully understood.

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